i BYZANTINE ARCHITECTURE 21 constructed with the lightest of centering, the surfaces and curves must have been largely determined by the mason as he built, and would not necessarily follow any definite geometrical development. cc II serait illusoire," remarks Choisy, ad'attribuer k toutes les voutes byzantines un trace g£o-m£trique rigoureusement d£fini." 1 The vaults commonly found are the barrel vault, the cross-groined vault, and the dome-vault. The first is frequently used over the cross arms and the bema, and sometimes over the narthex in conjunction with the groined vault (Diaconissa). It is the simplest method of covering an oblong space, but it does not easily admit of side windows above the springing. • . A very beautiful form of cross-groined vault is found in S. Sophia and in SS. Sergius and Bacchus, in which the crown is considerably domed, and the groins, accordingly, lose themselves in the vaulting surface. This form is found in Greek churches of late date, but does not occur in the later churches of Constantinople. A full description of the form and construction is given by Choisy2 and by Lethaby and Swainson.3 The cross-groined vault as found in the Myrelaion and many other churches of the city is level in the crown, with clearly marked groins. It is sometimes used with transverse arches resting on pilasters, or without these adjuncts. One of the most interesting of the vault forms is the dome-vault, a shallow dome with continuous pendentives. It is distinguished in appearance from the groined vault, as found in S. Sophia, by the absence of any groin line, and is completely different in construction. The geometrical construction is that of the pendentives of all domes. The four supporting arches intersect a hemispherical surface whose diameter is equal to the diagonal of the supporting square. The pendentives produce at the crown line of the arches a circular 'plan which is filled in by a saucer dome of the same radius as the pendentives, constructed of circular brick rings, the joints of 1 UArtde batir che* les Byxantins, p. 57. 2 Ibid. p. 99. 3 Sancta Sophia, p. 219.